Population prediction method and device based on combination of ARIMA model and queue element method

Abstract

The invention relates to the technical field of population prediction, and discloses a population prediction method and device based on combination of an ARIMA model and a queue element method. The method comprises the steps of obtaining historical migration population data of a to-be-predicted region, determining a difference order through ADF test, preliminarily determining the range of an autoregression order and a moving average order by using an autocorrelation function and a partial autocorrelation function, and constructing an ARIMA model; the optimized ARIMA model is adopted to fit historical migration population data, a migration population prediction result is obtained, and migration population data of each age group in the target prediction time period is output in combination with age structure data of floating population of the reference year; taking the migration population data of each age group as input parameters of migration population in a queue element method; according to a preset sum growth rate, selecting a western mode of a numeral-demann region model life table as a death model; and setting the average life expectancy according to a preset birth ratio, and realizing permanent resident population prediction of the to-be-predicted region.

Description

Technical Field

[0001] The present application relates to the technical field of population forecasting, and in particular to a population forecasting method and device based on the combination of an ARIMA model and a cohort factor method. Background Art

[0002] In the field of population forecasting, the cohort factor method is a commonly used age- and gender-specific forecasting method. Its core goal is to achieve long-term forecasts by simulating the birth, death, and migration processes of the population. However, the traditional cohort factor method has the following shortcomings when dealing with migrant populations:

[0003] 1. Migrant population forecasts rely on fixed ratios or simple trend extrapolation, failing to fully capture the dynamic characteristics of time series (such as periodicity and random fluctuations), resulting in low forecast accuracy;

[0004] 2. The setting of key parameters (such as total fertility rate and mortality model) lacks clear policy basis and standardized procedures, resulting in large differences in different prediction results, making it difficult to support policy optimization.

[0005] In existing technologies, solutions that only use cohort element methods or simple time series models (such as linear regression) cannot effectively solve the complex dynamic prediction problems of migrant populations, resulting in deviations between the permanent population predictions of target areas (such as cities) and the actual situation, which in turn affects the scientific nature of population policies.

[0006] Therefore, a method is urgently needed to solve at least one of the above problems. Summary of the Invention

[0007] This application provides a population forecasting method and device based on the combination of the ARIMA model and the cohort element method, aiming to solve the problem in the existing technology that the solutions using only the cohort element method or simple time series models (such as linear regression) are unable to effectively solve the complex dynamic forecasting problem of migrant population, resulting in deviations between the permanent population forecast of the target area (such as a city) and the actual situation, thereby affecting the scientific nature of the population policy.

[0008] In a first aspect, the present application provides a population forecasting method based on a combination of an ARIMA model and a cohort factor method, including:

[0009] Obtain historical migrant population data for the area to be predicted, determine the difference order through the ADF test, preliminarily determine the range of the autoregressive order and the moving average order using the autocorrelation function and the partial autocorrelation function, and construct an ARIMA model; optimize the model parameters of the ARIMA model through cross-validation, select the optimal parameters based on the Akaike Information Criterion, fit the historical migrant population data using the optimized ARIMA model, predict the migrant population in the target prediction time period, and obtain the migrant population prediction result;

[0010] The migration population prediction result is used as input, combined with the age structure data of the floating population in the base year, to output the migration population data of each age group within the target prediction period; the migration population data of each age group is used as the input parameter of the migration population in the cohort factor method;

[0011] According to the preset total fertility rate, the western model of the Coleman-Derman regional model life table is selected as the death model; the average life expectancy is set according to the preset sex ratio at birth; the input parameters are input into the cohort element method model together with the total fertility rate, death model, sex ratio at birth, and average life expectancy to realize the permanent population prediction of the area to be predicted.

[0012] In some embodiments, the method of determining the differential order through the ADF test, preliminarily determining the range of the autoregressive order and the moving average order using the autocorrelation function and the partial autocorrelation function, and constructing the ARIMA model includes: taking the historical migrant population data as input, performing a stationarity test on the historical migrant population data, and determining the differential order required to stabilize the data through the ADF test; based on the stabilized data, determining the potential range of the moving average order by analyzing the tailing or truncation characteristics of the autocorrelation function, determining the potential range of the autoregressive order by analyzing the tailing or truncation characteristics of the partial autocorrelation function, and constructing the ARIMA model based on the differential order, the autoregressive order range, and the moving average order range.

[0013] In some embodiments, the method of optimizing the model parameters of the ARIMA model through cross-validation and selecting the optimal parameters based on the Akaike Information Criterion includes: dividing the historical migration population data into a training set and a validation set, cross-validating the ARIMA model of multiple parameter combinations, and evaluating the model performance by calculating the prediction error of the validation set; calculating the Akaike Information Criterion value for each parameter combination, and selecting the parameter combination with the smallest Akaike Information Criterion value as the optimal parameter of the ARIMA model.

[0014] In some embodiments, the optimized ARIMA model is used to fit the historical migrant population data to predict the migrant population in the target prediction time period to obtain the migrant population prediction result, including: using the ARIMA model to perform time series fitting on the historical migrant population data to extract trend, seasonality and random characteristics in the data; based on the fitted ARIMA model, an extrapolated prediction is performed on the migrant population in the target prediction time period, and the migrant population prediction result including the number of migrant population at each prediction time point is output.

[0015] In some embodiments, the selection of the western model of the Coldman regional model life table as the death model includes: based on the population death characteristics of the area to be predicted, selecting the western model in the Coldman regional model life table that matches the area to be predicted as a death probability calculation model, and the death model is used to predict the mortality rate of the population in each age group.

[0016] In some embodiments, setting the average life expectancy based on a preset sex ratio at birth includes: based on the sex ratio at birth corresponding to the area to be predicted, the sex ratio at birth is used to calculate the male-female ratio of newborns; based on preset empirical data on population life expectancy growth, setting the average life expectancy of each gender in the area to be predicted according to the average growth step, and the average life expectancy is used to correct the calculation parameters of the population survival probability.

[0017] In some embodiments, the input parameters are input together with the total fertility rate, death model, sex ratio at birth, and average life expectancy into the cohort element method model to realize the permanent population prediction of the area to be predicted, including: based on the population balance equation of the cohort element method, the migrant population data of each age group, the total fertility rate, the mortality rate output by the death model, the sex ratio at birth and the average life expectancy are used as input parameters, and through age- and sex-based population dynamics simulation, the number of births, deaths, migrants and existing population in each year within the target prediction time period is calculated; by iteratively calculating the population stock of each year, the permanent population prediction result of the area to be predicted within the target prediction time period is finally output.

[0018] In a second aspect, the present application provides a population forecasting device based on a combination of an ARIMA model and a cohort factor method, the device comprising:

[0019] A data acquisition unit is used to obtain historical migrant population data of the area to be predicted, determine the difference order through the ADF test, preliminarily determine the range of the autoregressive order and the moving average order using the autocorrelation function and the partial autocorrelation function, and construct an ARIMA model; optimize the model parameters of the ARIMA model through cross-validation, select the optimal parameters based on the Akaike Information Criterion, use the optimized ARIMA model to fit the historical migrant population data, predict the migrant population in the target prediction time period, and obtain the migrant population prediction result;

[0020] A result input unit is used to take the migrant population prediction result as input, combine it with the age structure data of the floating population in the base year, and output the migrant population data of each age group within the target prediction time period; and use the migrant population data of each age group as the input parameter of the migrant population in the cohort factor method;

[0021] The prediction completion unit is configured to select a west mode of a Coale and Dema- n's regional model life table as a death model according to a preset total fertility rate, set an average life expectancy according to a preset birth sex ratio, and input the input parameters, the total fertility rate, the death model, the birth sex ratio and the average life expectancy into a cohort-component model to realize the resident population prediction of the to-be-predicted region.

[0022] In a third aspect, the present application provides a computer device, comprising a memory and a processor, wherein the memory stores computer readable instructions, and the computer readable instructions are executed by the processor to make the processor perform the steps of the method provided by any of the embodiments of the present application.

[0023] In a fourth aspect, the present application provides a computer readable storage medium, wherein the computer readable storage medium stores a computer program, and the computer readable instructions are executed by the processor to make one or more processors perform the steps of the method provided by any of the embodiments of the present application.

[0024] The embodiments of the present application provide a population prediction method combining an ARIMA model and a cohort-component method, comprising: ARIMA model construction and optimization: determining model order through ADF test and ACF / PACF analysis, optimizing parameters by cross-validation and AIC criterion, realizing time series fitting of historical migration population data and migration population prediction in a target time period; age-specific migration population generation: based on the age structure of the baseline year floating population, decomposing the total migration population predicted by the ARIMA into age-specific data; cohort-component method parameter integration: setting total fertility rate and birth sex ratio according to policy documents, adopting Coale and Deman's west mode as a death model, setting average life expectancy according to United Nations experience value, finally inputting the above parameters into the cohort-component method model to realize dynamic prediction of the resident population of the target region in terms of age and gender.

[0025] Through ARIMA model time series dynamic modeling of migration population (including difference processing and parameter optimization), the problem of insufficient capture of randomness and trend of migration population prediction in traditional methods is solved, and the prediction accuracy of migration population and resident population is significantly improved; the total fertility rate, birth sex ratio and other key parameters are directly related to national and local population development planning, the death model and average life expectancy adopt internationally recognized standards (Coale and Deman model, United Nations experience value), so that the prediction process has more policy basis and standardized features; through age-specific migration population simulation and dynamic prediction of resident population, scientific and quantitative basis is provided for population planning, public service allocation and other policy optimization of the target region (such as a city), and the deficiencies of the prior art in the policy analysis level are made up.

[0026] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the description of the embodiments. Obviously, the drawings described below are some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0028] Figure 1 This is a schematic flow chart of the steps of a population forecasting method based on the combination of the ARIMA model and the cohort factor method provided in one embodiment of the present application;

[0029] Figure 2 This is a schematic block diagram of a population prediction device based on the combination of the ARIMA model and the cohort factor method provided in one embodiment of the present application;

[0030] Figure 3 This is a schematic block diagram of the structure of a computer device provided in one embodiment of the present application.

[0031] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present application. DETAILED DESCRIPTION

[0032] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0033] The flowcharts shown in the accompanying drawings are for illustrative purposes only and do not necessarily include all contents and operations / steps, nor must they be executed in the order described. For example, some operations / steps may be decomposed, combined, or partially merged, so the actual execution order may vary depending on the actual situation.

[0034] It should be understood that the terms used in this specification are only for the purpose of describing specific embodiments and are not intended to limit the present application. As used in this specification and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0035] It should be further understood that the term “and / or” used in this specification and the appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0036] The following describes some embodiments of the present application in detail with reference to the accompanying drawings. In the absence of conflict, the following embodiments and features therein may be combined with each other.

[0037] In the field of population forecasting, the cohort factor method is a commonly used age- and gender-specific forecasting method. Its core goal is to achieve long-term forecasts by simulating the birth, death, and migration processes of the population. However, the traditional cohort factor method has the following shortcomings when dealing with migrant populations:

[0038] 1. Migrant population forecasts rely on fixed ratios or simple trend extrapolation, failing to fully capture the dynamic characteristics of time series (such as periodicity and random fluctuations), resulting in low forecast accuracy;

[0039] 2. The setting of key parameters (such as total fertility rate and mortality model) lacks clear policy basis and standardized procedures, resulting in large differences in different prediction results, making it difficult to support policy optimization.

[0040] In existing technologies, solutions that only use cohort element methods or simple time series models (such as linear regression) cannot effectively solve the complex dynamic prediction problems of migrant populations, resulting in deviations between the permanent population predictions of target areas (such as cities) and the actual situation, which in turn affects the scientific nature of population policies.

[0041] Therefore, a method is urgently needed to solve at least one of the above problems.

[0042] To resolve the above issues, please refer to Figure 1 , Figure 1 This is a flowchart illustrating the steps of a population forecasting method based on the ARIMA model combined with the cohort factor method, provided in one embodiment of the present application. This method can be implemented using a computer device, which can be deployed on a single server or a server cluster. Alternatively, it can be deployed on a handheld terminal, laptop computer, wearable device, or robot.

[0043] It should be noted that any information involved in the embodiments of the present application complies with relevant policies and regulations and is carried out with the authorization and permission of relevant users, and will not infringe on the privacy of users.

[0044] like Figure 1 As shown, the population forecasting method based on the combination of the ARIMA model and the cohort factor method specifically includes steps S101 to S103:

[0045] Step S101: Obtain historical migrant population data for the area to be predicted, determine the difference order through the ADF test, preliminarily determine the range of the autoregressive order and the moving average order using the autocorrelation function and the partial autocorrelation function, and construct an ARIMA model; optimize the model parameters of the ARIMA model through cross-validation, select the optimal parameters based on the Akaike Information Criterion, use the optimized ARIMA model to fit the historical migrant population data, predict the migrant population in the target prediction time period, and obtain the migrant population prediction result.

[0046] Specifically, this step constructs an ARIMA model using time series analysis to dynamically model historical migrant population data, capturing the cyclical and random fluctuations of this population. The core process includes testing for data stationarity (ADF test), preliminary determination of the model order (using the autocorrelation function (ACF) and partial autocorrelation function (PACF), parameter optimization (using cross-validation and the Akaike Information Criterion (AIC), and forecasting applications).

[0047] This step specifically includes data preprocessing and stationarity testing: Collect historical migration data (e.g., annual or quarterly data) for the region to be predicted, address outliers, and interpolate missing values. Use the ADF test (Augmented Dickey-Fuller Test) to determine data stationarity. If the data is nonstationary, perform differencing (first-order or multi-order) to make it stationary and determine the differencing order (dd) (i.e., the dd parameter in the ARIMA model).

[0048] Preliminary determination of the model order: Plot the ACF and PACF of the stationary data to observe the truncation or tailing characteristics of the autocorrelation and partial autocorrelation. If the PACF is truncated after order p, preliminarily determine the range of the autoregressive order pp; if the ACF is truncated after order q, preliminarily determine the range of the moving average order q. Based on operational experience (such as the possible annual cyclicality of migration), set candidate intervals for p and q (e.g., p∈[0,3], q∈[0,3]).

[0049] Model construction and parameter optimization: For each (p, d, q) combination, an ARIMA model is constructed. Cross-validation (such as time series cross-validation to prevent future data leakage) is used to evaluate the model's prediction error (such as root mean square error (RMSE)) on the training set. The optimal model parameters are selected based on the AIC criterion: the smaller the AIC value, the better the model fit and the lower the complexity. Ultimately, the optimal p, d, q values ​​are determined.

[0050] Model Fitting and Forecasting: Use the optimized ARIMA model to fit historical migration data and verify the model's ability to capture historical fluctuations (e.g., residual analysis). Extrapolate forecasts for the target forecast period (e.g., the next 10 years) to generate a migration forecast series (e.g., annual inbound and outbound population totals).

[0051] Through differencing and order optimization of the ARIMA model, we effectively capture both cyclical (such as fluctuations in migration around the Spring Festival) and random fluctuations in the population, avoiding the limitations of traditional fixed ratios or simple trend extrapolation and improving forecast accuracy. Parameter selection based on cross-validation and the AIC criterion reduces the subjectivity of manual parameter adjustment, ensuring the model's optimal fit to historical data and providing more reliable input parameters for the subsequent cohort factor method.

[0052] Step S102: taking the predicted result of the migrant population as input, combining it with the age structure data of the floating population in the base year, outputting the migrant population data of each age group within the target prediction time period; taking the migrant population data of each age group as the input parameter of the migrant population in the cohort element method.

[0053] Specifically, by distributing the total number of migrants predicted by the ARIMA model according to the age structure of the floating population in the base year, we generate data on migrants by age group, which serve as the input parameters for the age- and sex-specific migration in the cohort factor method. The core of this approach is to decompose the total number into specific age groups using age structure proportions, ensuring that the age distribution of migrants conforms to historical patterns.

[0054] This step specifically includes: Obtaining age structure data for the base year: Collecting migrant population census or sampling survey data for the base year (such as the starting year of the forecast), extracting the population size and proportion of each age group (such as a group of 5 years old, 0-4 years old, 5-9 years old... 65+ years old), and forming an age structure distribution matrix (gender optional).

[0055] Decomposition of the total amount into age groups: For each year in the target forecast period, assuming that the age structure of the migrant population is consistent with that of the base year (or dynamically adjusted according to trends, such as gradually approaching the age structure of the permanent population), the migrant population in each age group is calculated according to the following formula: Migrant population in age group i = total migrant population in that year × proportion of migrant population in age group i in the base year; if the trend of changes in the age structure needs to be considered, a correction coefficient can be introduced (such as fitting the age structure change function through historical data), but the proportion of the base year is preferred in initial implementation to reduce complexity.

[0056] Input Cohort Element Method: Age-specific migrant population data is organized by in-migration and out-migration, serving as input parameters for the "Migration Module" within the cohort element method and integrating with the age-specific population stock in the original cohort model. Traditional cohort element methods often use a uniform migration rate, ignoring age differences (e.g., higher migration rates for the working-age population). This step, however, uses age-structured allocation to make the distribution of migrants more realistic and improve the accuracy of population stock calculations within the cohort model (e.g., the impact of working-age population growth on urban development is more realistic). Combining the aggregate forecasting of ARIMA with the age-specific structure requirements of the cohort element method overcomes the inability of single time series models to forecast by age, creating a closed loop of "dynamic aggregate forecasting → refined structural allocation."

[0057] Step S103: Based on the preset total fertility rate, the western model of the Coleman-Derman regional model life table is selected as the death model; the average life expectancy is set according to the preset sex ratio at birth; and the input parameters together with the total fertility rate, death model, sex ratio at birth, and average life expectancy are input into the cohort factor method model to realize the resident population prediction of the area to be predicted.

[0058] Specifically, by setting core parameters such as fertility, death, and migration under the framework of the cohort factor method, parameters such as the total fertility rate (TFR), mortality model (Cole-Derman Western model), sex ratio at birth (SRB), and life expectancy (LE) are determined based on policy basis and standardized processes to ensure the policy support of the prediction results.

[0059] This step specifically includes: Fertility parameter setting: Total fertility rate (TFR): Preset the TFR (e.g., 1.8-2.1) based on the target region's population policies (e.g., supporting measures for the three-child policy), historical fertility trends, and expert consensus to avoid subjectivity and arbitrariness. For example, TFRs can be set under different scenarios (e.g., baseline scenario, relaxed scenario) in conjunction with population development planning goals.

[0060] Mortality model selection: The "Western model" of the Coleman-Derman regional life table model was used, which is suitable for regions with moderate mortality levels. Model parameters were calibrated based on age- and sex-specific mortality data to generate mortality probabilities for each age group.

[0061] Sex Ratio at Birth (SRB) and Life Expectancy (LE): The SRB is set based on advocated gender equality goals and historical data (e.g., a normal range of 105-107) to avoid demographic bias caused by extreme values. Life expectancy is determined based on regional healthcare development trends, United Nations population prospects, or health planning goals (e.g., increasing life expectancy to 79 years by 2030), to determine the growth path for life expectancy by sex.

[0062] The cohort element method integrates forecasting: Using the age- and sex-specific population of the base year as the initial cohort, the method performs annual recursive forecasting. The fertility module calculates the number of births to women of childbearing age in each age group based on the TFR and SRB. The mortality module calculates the survival probability of each age group based on the mortality model and updates the surviving population. The migration module inputs the age-specific migrant population generated in step S102 and adjusts the population inventory. Finally, the target year's age- and sex-specific population forecast is output. Core parameters (such as TFR and mortality model) are set based on clear policy support (e.g., population development plans) and standardized processes (e.g., using authoritative life table models). This reduces parameter variations across studies, makes forecast results comparable, and facilitates reference for policymakers.

[0063] Combining dynamic migration prediction with standardized fertility and mortality models can solve the problems of rough migration processing and highly subjective parameters in traditional cohort methods, forming a comprehensive prediction framework of "data-driven migration prediction + policy-oriented core parameters", and improving the scientific nature and policy relevance of permanent population prediction.

[0064] In some embodiments, the method of determining the differential order through the ADF test, preliminarily determining the range of the autoregressive order and the moving average order using the autocorrelation function and the partial autocorrelation function, and constructing the ARIMA model includes: taking the historical migrant population data as input, performing a stationarity test on the historical migrant population data, and determining the differential order required to stabilize the data through the ADF test; based on the stabilized data, determining the potential range of the moving average order by analyzing the tailing or truncation characteristics of the autocorrelation function, determining the potential range of the autoregressive order by analyzing the tailing or truncation characteristics of the partial autocorrelation function, and constructing the ARIMA model based on the differential order, the autoregressive order range, and the moving average order range.

[0065] This embodiment specifically includes: Data input and stationarity testing: Historical migration population data (e.g., in-migration and out-migration statistics by year or quarter) is used as model input. Data cleaning is first performed (dealing with outliers and filling missing values). The cleaned data is then tested for stationarity using the ADF test to determine whether the data meets stationarity requirements (i.e., the mean, variance, and autocovariance do not change over time). If the p-value of the ADF test is greater than the significance level (e.g., 0.05), the data is non-stationary and requires differencing (first-order or multiple-order differencing) until the ADF test indicates that the data is stationary. The required differencing order d is recorded.

[0066] Determine the order range: Plot the autocorrelation function (ACF) and partial autocorrelation function (PACF) of the stationary data. Observe the ACF for tailing or truncation. If the ACF significantly decays (truncates) after order qq, the potential range of the moving average order q is near the truncation order (e.g., if truncated at order 2, q can be 0, 1, or 2). If the ACF exhibits tailing, q needs to be determined through subsequent parameter optimization. Observe the PACF for tailing or truncation. If the PACF truncates after order p, the potential range of the autoregressive order p is near the truncation order (e.g., if truncated at order 3, p can be 0, 1, 2, or 3). If the PACF exhibits tailing, p needs to be determined through parameter optimization. Based on business experience (such as the possible annual periodicity of the migration data), initially limit the search range of p and q (e.g., p∈[0,4], q∈[0,4]).

[0067] Construct an ARIMA model: Based on the determined differencing order d, autoregressive order range p, and moving average order range q, generate all possible (p, d, q) parameter combinations (e.g., p = 0, 1, 2; d = 1; q = 0, 1, 2) and construct the corresponding ARIMA model.

[0068] The ADF test quantitatively determines data stationarity, avoiding the subjective nature of empirically setting differencing orders. This ensures that the time series meets the requirements for the ARIMA model and lays the foundation for subsequent modeling. The statistical properties of the ACF and PACF are used to automatically identify the potential range of orders. Incorporating the inherent patterns of time series (such as periodicity and correlation) narrows the parameter search space, improves model building efficiency, and reduces ineffective trial and error.

[0069] In some embodiments, the method of optimizing the model parameters of the ARIMA model through cross-validation and selecting the optimal parameters based on the Akaike Information Criterion includes: dividing the historical migration population data into a training set and a validation set, cross-validating the ARIMA model of multiple parameter combinations, and evaluating the model performance by calculating the prediction error of the validation set; calculating the Akaike Information Criterion value for each parameter combination, and selecting the parameter combination with the smallest Akaike Information Criterion value as the optimal parameter of the ARIMA model.

[0070] This embodiment specifically includes: Data partitioning and cross-validation: Historical migration population data is divided into a training set (for model fitting) and a validation set (for model evaluation) in chronological order. "Time series cross-validation" methods (such as rolling window validation, to avoid chronological confusion caused by random partitioning) are typically used. For example, the first 80% of the data is used as the training set, and the last 20% as the validation set. The ARIMA models for all generated (p, d, q) parameter combinations are sequentially fitted on the training set, and then predictions are performed on the validation set to calculate the prediction error (such as root mean square error (RMSE) and mean absolute error (MAE)).

[0071] Akaike Information Criterion (AIC) Calculation and Parameter Selection: For each parameter combination, calculate the AIC value: AIC = 2k − 2ln(L), where k is the number of model parameters and L is the model log-likelihood. Smaller AIC values ​​indicate better model fit and lower model complexity. Compare the AIC values ​​for all parameter combinations and select the combination with the lowest AIC value as the optimal parameter for the ARIMA model (e.g., p = 2, d = 1, q = 1).

[0072] The validation set error quantifies the model's generalization ability, avoiding overfitting caused by relying solely on the training set and ensuring the model's predictive reliability on unknown data. The AIC criterion automatically selects optimal parameters, eliminating the subjectivity of manual parameter adjustment. This balances model accuracy and complexity, improving the stability of migrant population prediction.

[0073] In some embodiments, the optimized ARIMA model is used to fit the historical migrant population data to predict the migrant population in the target prediction time period to obtain the migrant population prediction result, including: using the ARIMA model to perform time series fitting on the historical migrant population data to extract trend, seasonality and random characteristics in the data; based on the fitted ARIMA model, an extrapolated prediction is performed on the migrant population in the target prediction time period, and the migrant population prediction result including the number of migrant population at each prediction time point is output.

[0074] This embodiment specifically includes: Time series fitting and feature extraction: Using an optimized ARIMA model to fit the entire sample of historical migration population data, the model parameters (autoregressive coefficients, moving average coefficients) are used to capture trends (such as long-term growth or decline), seasonality (such as the migration peak around the Spring Festival), and random fluctuations (such as abnormal fluctuations caused by sudden policy impacts) in the data. The fitted residual sequence is output and a white noise test (such as the LB test) is used to verify whether the residual is white noise (no significant correlation) to ensure that the model has fully extracted the data features.

[0075] Extrapolation and Result Output: Based on the fitted ARIMA model, the target prediction period (e.g., the next 10 years) is recursively predicted. During prediction, the predicted value of the previous time point is taken as the input for subsequent prediction, and the migration population at each prediction time point (e.g., 2026 migration-in, 2027 migration-out, etc.) is gradually extrapolated. The migration population prediction results are output in the form of sequence data (e.g., CSV table or array) containing timestamps (year / quarter) and corresponding migration amounts, for use in subsequent steps.

[0076] Through model fitting, multiple features of migration data are extracted, which can more accurately depict migration dynamics (such as the amplitude and frequency of periodic fluctuations) compared to traditional simple trend extrapolation, solving the problem of ignoring short-term fluctuations in the fixed proportion method. It provides specific migration amount prediction at each time point, providing high-precision input for age-specific and time-specific migration population allocation in the cohort component method, and improving the accuracy of subsequent population stock calculation.

[0077] In some embodiments, the selected west mode of the Coale and Demeny regional model life table is used as a death model, including: selecting the west mode of the Coale and Demeny regional model life table that matches the to-be-predicted region as the death probability calculation model for the population death characteristics of the to-be-predicted region, and the death model is used to predict the mortality rate of each age group population.

[0078] This embodiment specifically includes: death model matching: analyzing the population death characteristics (such as infant mortality rate, old-age population mortality level) of the to-be-predicted region, comparing different modes (west, east, south, etc.) of the Coale and Demeny regional model life table, and selecting the "west mode" (suitable for medium mortality rate and gradually improving life expectancy) that best matches the development level and medical conditions of the region. Obtain the historical mortality rate data of the to-be-predicted region by age and gender from authoritative data sources, and calibrate the basic parameters (such as the initial value of infant mortality rate and the mortality probability growth rate of each age group) in the west mode to ensure that the model fits the local actual situation.

[0079] Mortality prediction application: the death model inputs age x and gender s, and outputs the mortality rate mx,s of the corresponding age group, which is used for the calculation of survival probability in the cohort component method: lx+1,s=lx, , where lx,s is the number of surviving people of age x and gender s.

[0080] The internationally recognized Coleman-Derman model and regionalized model were adopted to avoid the arbitrariness of mortality models across different studies, establish a unified standard for mortality predictions, and enhance the comparability of population predictions across different regions. The Western model was selected and parameters were calibrated based on regional characteristics to ensure that mortality probabilities are consistent with local population health levels, avoid errors in population survival calculations caused by deviations in mortality models, and improve the reliability of the underlying data from the cohort factor method.

[0081] In some embodiments, setting the average life expectancy based on a preset sex ratio at birth includes: based on the sex ratio at birth corresponding to the area to be predicted, the sex ratio at birth is used to calculate the male-female ratio of newborns; based on preset empirical data on population life expectancy growth, setting the average life expectancy of each gender in the area to be predicted according to the average growth step, and the average life expectancy is used to correct the calculation parameters of the population survival probability.

[0082] This embodiment specifically includes: Setting the sex ratio at birth (SRB): Based on the policy orientation of the region being predicted (e.g., implementing gender equality and curbing fetal sex identification) and historical data, a reasonable SRB (e.g., 105-107, representing the number of male babies born for every 100 female babies) is preset. For example, if the local SRB was 106 in recent years, this value will be used as the parameter for the prediction period, or gradually adjusted to a normal range based on policy objectives. The sex ratio of newborns is calculated based on the SRB: male baby ratio = SRB / (100 + SRB), female baby ratio = 100 / (100 + SRB).

[0083] Life expectancy (LE) setting: Historical life expectancy data for the region under prediction, broken down by sex (e.g., 75 years for men and 79 years for women), are collected. Based on the life expectancy growth target (e.g., an average annual increase of 0.1-0.2 years for life expectancy), an average growth step size (e.g., 0.15 years per year for men and 0.1 years per year for women) is set. Life expectancy for each year by sex is recursively calculated using the following formula: LEt,s = LEbase year,s + growth step size s × (t-base year), where t is the prediction year and s is sex (male / female). Life expectancy is used to modify the survival probability parameters in mortality models; for example, higher life expectancy corresponds to lower mortality rates for each age group.

[0084] By rationally setting the SRB, we can avoid demographic imbalances caused by extreme sex ratios (such as problems in the marriage market caused by an excess of males) and ensure that the sex distribution of newborns aligns with sustainable social development goals. By setting a life expectancy growth path based on empirical data and policy objectives, we can dynamically adjust mortality model parameters as population health improves, more realistically reflecting the changing trends in population survival probabilities and avoiding the forecast biases associated with fixed mortality rate assumptions.

[0085] In some embodiments, the input parameters are input together with the total fertility rate, death model, sex ratio at birth, and average life expectancy into the cohort element method model to realize the permanent population prediction of the area to be predicted, including: based on the population balance equation of the cohort element method, the migrant population data of each age group, the total fertility rate, the mortality rate output by the death model, the sex ratio at birth and the average life expectancy are used as input parameters, and through age- and sex-based population dynamics simulation, the number of births, deaths, migrants and existing population in each year within the target prediction time period is calculated; by iteratively calculating the population stock of each year, the permanent population prediction result of the area to be predicted within the target prediction time period is finally output.

[0086] This embodiment specifically includes: Construction of the core equation of the cohort element method: Based on the population balance equation, a dynamic model is established by age and gender: Where: Nx,t,s is the population of x-year-old and sex s in year t; Mx,t,s is the net number of migrants of x-year-old and sex s in year t (derived from age-specific migration data). Fertility module: Calculate the number of births in each year based on the total fertility rate (TFR) and SRB: , where fxfx is the fertility rate for women aged xx years, distributed to each age group using the TFR. The mortality module: This module invokes the mortality model to calculate the probability of death for each age group and updates the surviving population. The migration module: This module inputs the generated age-specific migration data and adjusts the population stock for each age group (in-migration is positive, out-migration is negative). Starting from the baseline year, the calculation is iterated year by year until the target forecast year, recording the population counts by age and sex in each year and summing them up to obtain the total permanent population.

[0087] Result output: The final output is the permanent population forecast results for each year within the target forecast period, including the total number and age and gender structure data (such as Excel tables, database records), to support policy analysis (such as changes in the labor force and the degree of aging).

[0088] The cohort element method systematically integrates the three major demographic dynamics of migration, fertility, and mortality. Parameters for each module are set based on scientific methods or policy considerations (migration is derived from ARIMA dynamic forecasts, and fertility and mortality are derived from standardized models). This creates a logically closed loop, preventing bias in a single module from influencing the overall forecast. Age- and gender-specific forecasts can be directly used to evaluate the effectiveness of population policies (such as the impact of fertility policies on the number of births and the role of migration policies on labor force concentration). This provides refined data support for government policies on education resource allocation, elderly care facility planning, and other areas, enhancing scientific decision-making.

[0089] In some embodiments, a traditional ARIMA model is combined with a long short-term memory network (LSTM) to build a hybrid model to capture linear trends and nonlinear complex patterns in migration population data. ARIMA handles the linear part of the data (such as periodic fluctuations), and LSTM handles the nonlinear part (such as policy mutations, economic cycles, and other unstructured influences). The two prediction results are fused through an error correction mechanism to improve the prediction accuracy in complex dynamic scenarios.

[0090] This embodiment specifically includes: data feature decomposition: after the historical migration population data is differentially smoothed, the linear trend component (suitable for ARIMA modeling) and the nonlinear fluctuation component (suitable for LSTM modeling) are separated through empirical mode decomposition (EMD) or Fourier transform.

[0091] Dual-model parallel modeling: ARIMA branch: build an ARIMA model for the linear component, determine the optimal parameters (p, d, q) through ACF / PACF and AIC, and output the linear trend prediction value. LSTM branch: convert the nonlinear component into a time series matrix (input dimension is [sample number, time step, feature number]), design an LSTM network (such as 2 layers of 128 units, dropout=0.2), use the Adam optimizer for training, and output the nonlinear fluctuation prediction value.

[0092] Error correction and result fusion: calculate the residual error between the true value of the historical data and the prediction value of the dual model, build a residual prediction model (such as linear regression), and correct the final prediction result: final prediction value = ARIMA prediction value + LSTM prediction value + residual correction value.

[0093] Breaking the linear assumption limit of traditional ARIMA, capturing nonlinear influences such as policy changes and sudden events (such as a sharp drop in migration due to an epidemic) through LSTM, combining the periodic modeling advantages of ARIMA, achieving complementary prediction of "linear trend + nonlinear fluctuation", especially suitable for areas with dramatic data fluctuations or structural mutations. The residual correction mechanism reduces systematic bias of the model, maintains high prediction accuracy when data volume is small or there is noise, and provides more reliable migration population input for the cohort element method.

[0094] In some embodiments, the Facebook Prophet algorithm is used instead of the traditional ARIMA to quickly build a migration population prediction model by taking advantage of its automated seasonal analysis, holiday effect modeling, and robustness to outliers. The non-parametric model built into Prophet can automatically identify annual / seasonal periodicity, support flexible addition of external variables (such as GDP growth rate, hukou policy index), and does not require manual stationarity test and order selection, reducing the modeling threshold.

[0095] This embodiment specifically includes: data preprocessing and variable expansion: converting historical migration data into the (ds, y) format (timestamp, migration amount) required by Prophet, and adding external influencing factors (such as policy implementation year mark, economic indicator time series) as regression variables.

[0096] Prophet model configuration: Set seasonal cycles (e.g. yearly_seasonality=True, weekly_seasonality=False), configure holiday calendars (e.g. Spring Festival and National Day migration peaks), and control trend sensitivity through the changepoint_prior_scale parameter. Perform regression modeling on external variables: , where g(t) is the trend term, s(t) is the seasonal term, and h(xt) is the influence of external variables. For noise.

[0097] Prediction and uncertainty quantification: Use make_future_dataframe to generate a time series for the target prediction period, call the predict method to output the point prediction value and 80% / 95% confidence interval, and provide the cohort factor method with the migrant population input containing uncertainty.

[0098] Built-in algorithms automatically perform data conversion and model optimization, eliminating the need for manual stationarity processing and order selection. This significantly reduces technical implementation complexity and makes it suitable for rapid deployment by non-professionals. By integrating external variables into policy and economic factors (such as the immediate impact of relaxed household registration policies on inbound migration), forecasts are more realistic, addressing the limitations of traditional ARIMA models that rely solely on historical data and enhancing the policy relevance of forecasts.

[0099] In some embodiments, a K-means clustering algorithm is introduced to classify the historical age structure of migrant population and identify the age distribution patterns in different years (such as "young labor force-dominated" and "family migration"). During prediction, the most similar historical clustering pattern is dynamically matched according to current socioeconomic indicators (such as industrial structure and distribution of educational resources) to replace the fixed base year ratio and realize dynamic adaptive allocation of age structure.

[0100] This embodiment specifically includes: historical age structure clustering: collecting age ratio data of migrant population in each year of the past 20 years (such as the proportion of 15-29 years old, 30-44 years old, and over 45 years old), forming a feature matrix X∈Rn×3, using K-means algorithm clustering (preset K=3 typical modes), and marking the cluster category to which each year belongs.

[0101] Forecast Year Pattern Matching: The socioeconomic characteristics of the forecast year (e.g., the percentage of GDP in the secondary industry and the growth rate of the number of universities) are extracted as matching indicators. The cosine similarity with each historical cluster center is calculated, and the age structure proportion corresponding to the cluster with the highest similarity is selected. If new patterns emerge in the forecast year (e.g., aging migration trends), the new data is incorporated by dynamically updating the cluster centers.

[0102] Elastic allocation formula: Allocate the total number of migrants according to the matching cluster ratio, and introduce the elasticity coefficient αα (0.9-1.1) to adjust the extreme values: Migrant population in age group i = total number × (cluster ratio i × α).

[0103] Breaking the assumption of a fixed age structure, cluster matching captures evolving characteristics of the age distribution of migrants (e.g., rising proportions of young migrants due to industrial upgrading), avoiding allocation bias caused by outdated base year data and ensuring that the age-specific inputs of the cohort factor method are more aligned with current trends. Dynamically adjusting allocation ratios based on socioeconomic indicators directly links population migration to regional development needs (e.g., manufacturing cities require a young workforce), enhancing the guiding value of forecasts for urban planning.

[0104] In some embodiments, a Bayesian network is constructed to integrate the uncertainty of fertility, mortality, and migration parameters, and the total fertility rate (TFR) and life expectancy (LE) are set as random variables. The prior distribution is defined through historical data and expert knowledge (for example, TFR follows a normal distribution N(1.8, 0.152)). The Markov Chain Monte Carlo (MCMC) method is used to simulate the joint distribution of parameters to generate a cohort factor method prediction result that includes uncertainty. Specifically, it includes:

[0105] Bayesian network structure construction: Define nodes: TFR, LE (by gender), migration rate by age, and sex ratio at birth (SRB), and establish causal edges (e.g., TFR affects births, LE affects mortality). Set prior distributions: TFR uses the Beta distribution obtained from expert questionnaires, LE uses the lognormal distribution based on historical data, and migration rate uses the confidence interval of the prediction results in Example 1 converted to a truncated normal distribution.

[0106] Probabilistic Inference and Prediction: Use PyMC3 or the Stan framework to perform MCMC sampling (e.g., run 2000 iterations, discarding the first 500 burn-ins) to generate a set of parameter samples. Run the cohort factor method on each parameter sample to obtain the posterior distribution of the age-specific population forecast, and output the median prediction value and 95% prediction interval.

[0107] Policy scenario embedding: Add policy intervention nodes to the Bayesian network, evaluate the impact of policies on TFR through intervention analysis (do-calculus), and update the conditional probability distribution.

[0108] It breaks through the limitations of the traditional cohort method's "point prediction" and provides forecast results that include probability distribution (such as "there is a 70% probability that the working-age population will be between 8 and 9 million in 2035"), helping decision makers assess the risks of population change (such as the possibility of early onset of aging).

[0109] Through causal reasoning of Bayesian networks, the impact of different policies (such as fertility subsidies and talent introduction) on the population structure is quantified, supporting the full-link simulation of "policy-parameter-results" and enhancing the decision-making support capabilities of predictions.

[0110] In some embodiments, a non-dominated sorting genetic algorithm (NSGA-II) is introduced to perform multi-objective optimization on the core parameters of the cohort factor method (TFR, migration rate growth rate, and life expectancy growth rate). The optimization objectives are "the fit between the forecast results and historical data" and "the match between policy goals" (e.g., labor force retention rate ≥ 60%, aging rate ≤ 25%). This generates a Pareto optimal solution set, replacing a single parameter setting and supporting multi-scenario population forecasting. Specifically, this includes:

[0111] Objective function definition: Fitting objective: Minimize the root mean square error (RMSE) between historical population data and model output. Policy objective: Maximize the proportion of the working-age population (aged 15-64) and minimize the proportion of the population over 65, setting hard constraints (e.g., TFR∈[1.5, 2.3], migration rate∈[-5%, 10%]).

[0112] Genetic Algorithm Parameter Optimization: Encoding: Encode parameters such as TFR and migration rate growth rate into real vectors. Set the population size to 100 and the number of iterations to 50 generations. Fitness Calculation: Run the queue model for each parameter combination, calculate the value of the multi-objective function, and select the parent generation using non-dominated sorting and crowding distance.

[0113] Application of Pareto solution: Select the optimal parameter combination based on policy priorities (such as "maintaining the working population" or "controlling aging"), generate corresponding population forecast scenarios (such as the "high migration rate-medium fertility rate" scenario and the "low migration rate-high fertility rate" scenario), and output a population structure comparison report for each scenario.

[0114] This method breaks through the limitations of traditional cohort methods in parameter setting and generates forecasting scenarios that meet diverse policy objectives through multi-objective optimization, resolving the disconnect between forecast results and policy needs (e.g., high-migration scenario forecasting for attracting talent). It provides a diverse set of forecast solutions, supporting policymakers in weighing the pros and cons (e.g., high migration rates may boost the labor force in the short term but increase population dependence in the long term). This upgrades population forecasting from "outputting results" to "simulating decision-making scenarios," significantly enhancing its application value.

[0115] In some embodiments, a generative adversarial network (GAN) is constructed to simulate the complex dependency between the age structure and migration behavior of the floating population. Historical age-specific migration data is used as training samples. A generator generates an age-migration joint distribution that conforms to the true distribution. A discriminator distinguishes between the true data and the generated data, solving the age structure allocation problem in scenarios with small samples or missing data, and providing more realistic age-specific migration input for the cohort factor method. Specifically, this includes:

[0116] GAN model architecture design: Generator: Inputs a random noise vector z and predicted year features (such as year code and industrial structure index). Through a multi-layer fully connected network, it outputs an age-specific migration ratio vector p = (p1, p2, ..., pk), satisfying ∑pi = 1. Discriminator: Inputs a real / generated age ratio vector and outputs the probability of belonging to the real data. Wasserstein GAN is used to improve training stability.

[0117] Conditional constraints and data augmentation: By adding migration constraints to the generator (e.g., the generation ratio must match the ARIMA forecast), conditional GAN ​​(cGAN) is used to achieve "age structure generation under known totals." For years with missing data, GAN is used to generate reasonable age structures to supplement the historical dataset.

[0118] Migration-age joint input cohort model: The generated age-specific migration ratio is combined with the ARIMA total forecast to obtain the migrant population of each age group. When inputting the cohort factor method, the age-migration correlation is simultaneously considered (such as the indirect impact of the migration rate of 25-35 years old on the fertility rate).

[0119] For regions with incomplete data (e.g., lack of age-specific migration data at the county level), GANs are used to generate age structures consistent with the underlying distribution, avoiding the arbitrariness of relying on a single base year and filling data gaps. This captures the inherent connection between age and migration behavior (e.g., student migration is concentrated among 18-22-year-olds, while migrant workers are concentrated among 25-45-year-olds), generating age-specific migration patterns that are more realistic. This allows for more accurate calculation of dynamic interactions between age groups in cohort models (e.g., the contribution of young migrants to future fertility).

[0120] Referring to Figure 2 , Figure 2 is a structural schematic diagram of a population prediction device 200 provided by an embodiment of the present application, which is based on an ARIMA model combined with a cohort-component method. The population prediction device 200 is used to execute the steps of the population prediction method based on the ARIMA model combined with the cohort-component method shown in each of the embodiments. The population prediction device 200 can be a single server or a server cluster, or the population prediction device 200 can be a terminal, which can be a handheld terminal, a notebook computer, a wearable device, a robot, or the like.

[0121] As shown in Figure 2 , the population prediction device 200 based on the ARIMA model combined with the cohort-component method comprises:

[0122] A data acquisition unit 201 is configured to acquire historical migration population data of a region to be predicted, determine a difference order through ADF test, preliminarily determine a range of autoregressive order and moving average order by using autocorrelation function and partial autocorrelation function, and construct an ARIMA model; optimize model parameters of the ARIMA model through cross-validation, select optimal parameters based on Akaike information criterion, fit the historical migration population data by using the optimized ARIMA model, predict migration population in a target prediction period, and obtain a migration population prediction result;

[0123] A result input unit 202 is configured to input the migration population prediction result as an input, combine age structure data of a reference year's floating population, and output migration population data of each age group in the target prediction period; and input migration population data of each age group as an input parameter of migration population in the cohort-component method;

[0124] A prediction completion unit 203 is configured to select a western mode of a Coale-Demeny regional model life table as a death model according to a preset total fertility rate; set average life expectancy according to a preset birth sex ratio; and input the input parameter, the total fertility rate, the death model, the birth sex ratio, and the average life expectancy into a cohort-component method model, to realize prediction of permanent population of the region to be predicted.

[0125] In some embodiments, the method of determining the differential order through the ADF test, preliminarily determining the range of the autoregressive order and the moving average order using the autocorrelation function and the partial autocorrelation function, and constructing the ARIMA model includes: taking the historical migrant population data as input, performing a stationarity test on the historical migrant population data, and determining the differential order required to stabilize the data through the ADF test; based on the stabilized data, determining the potential range of the moving average order by analyzing the tailing or truncation characteristics of the autocorrelation function, determining the potential range of the autoregressive order by analyzing the tailing or truncation characteristics of the partial autocorrelation function, and constructing the ARIMA model based on the differential order, the autoregressive order range, and the moving average order range.

[0126] In some embodiments, the method of optimizing the model parameters of the ARIMA model through cross-validation and selecting the optimal parameters based on the Akaike Information Criterion includes: dividing the historical migration population data into a training set and a validation set, cross-validating the ARIMA model of multiple parameter combinations, and evaluating the model performance by calculating the prediction error of the validation set; calculating the Akaike Information Criterion value for each parameter combination, and selecting the parameter combination with the smallest Akaike Information Criterion value as the optimal parameter of the ARIMA model.

[0127] In some embodiments, the optimized ARIMA model is used to fit the historical migrant population data to predict the migrant population in the target prediction time period to obtain the migrant population prediction result, including: using the ARIMA model to perform time series fitting on the historical migrant population data to extract trend, seasonality and random characteristics in the data; based on the fitted ARIMA model, an extrapolated prediction is performed on the migrant population in the target prediction time period, and the migrant population prediction result including the number of migrant population at each prediction time point is output.

[0128] In some embodiments, the selection of the western model of the Coldman regional model life table as the death model includes: based on the population death characteristics of the area to be predicted, selecting the western model in the Coldman regional model life table that matches the area to be predicted as a death probability calculation model, and the death model is used to predict the mortality rate of the population in each age group.

[0129] In some embodiments, setting the average life expectancy based on a preset sex ratio at birth includes: based on the sex ratio at birth corresponding to the area to be predicted, the sex ratio at birth is used to calculate the male-female ratio of newborns; based on preset empirical data on population life expectancy growth, setting the average life expectancy of each gender in the area to be predicted according to the average growth step, and the average life expectancy is used to correct the calculation parameters of the population survival probability.

[0130] In some embodiments, the input parameters are input together with the total fertility rate, death model, sex ratio at birth, and average life expectancy into the cohort element method model to realize the permanent population prediction of the area to be predicted, including: based on the population balance equation of the cohort element method, the migrant population data of each age group, the total fertility rate, the mortality rate output by the death model, the sex ratio at birth and the average life expectancy are used as input parameters, and through age- and sex-based population dynamics simulation, the number of births, deaths, migrants and existing population in each year within the target prediction time period is calculated; by iteratively calculating the population stock of each year, the permanent population prediction result of the area to be predicted within the target prediction time period is finally output.

[0131] It should be noted that those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described devices and modules can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0132] The above-mentioned device can be realized in the form of a computer program. The computer program can be used in Figure 3 Runs on the computer device shown.

[0133] See also Figure 3 , Figure 3 FIG. 1 is a schematic block diagram of a computer device in one embodiment. The computer device may be a server.

[0134] See Figure 3 The computer device includes a processor, a memory, and a network interface connected through a system bus, wherein the memory may include a non-volatile storage medium and an internal memory.

[0135] The non-volatile storage medium can store an operating system and a computer program. The computer program includes program instructions, which, when executed, can cause a processor to execute any population forecasting method based on a combination of an ARIMA model and a cohort factor method.

[0136] The processor is used to provide computing and control capabilities and support the operation of the entire computer equipment.

[0137] The internal memory provides an environment for the operation of a computer program in a non-volatile storage medium. When the computer program is executed by a processor, the processor can execute any population forecasting method based on the combination of an ARIMA model and a cohort factor method.

[0138] The network interface is used for network communication, such as sending assigned tasks, etc. Those skilled in the art will understand that Figure 3The structure shown in the figure is only a block diagram of part of the structure related to the scheme of the present application, and does not constitute a limitation on the computer device to which the scheme of the present application is applied. The specific computer device can include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0139] It should be understood that the processor can be a central processing unit (CPU), and the processor can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor.

[0140] In one embodiment, the processor is configured to run a computer program stored in the memory to perform the following steps:

[0141] The historical migration population data of the to-be-predicted region is obtained, the difference order is determined through ADF test, the range of autoregressive order and moving average order is preliminarily determined by using autocorrelation function and partial autocorrelation function, and an ARIMA model is constructed; the model parameters of the ARIMA model are optimized through cross-validation, the optimal parameters are selected based on Akaike information criterion, the historical migration population data is fitted by using the optimized ARIMA model, the migration population in a target prediction period is predicted, and a migration population prediction result is obtained;

[0142] The migration population prediction result is taken as input, combined with the age structure data of the reference year's floating population, and the migration population data of each age group in the target prediction period is output; and each age group migration population data is taken as an input parameter of the migration population in the queue element method;

[0143] According to a preset total fertility rate, a western mode of a Coale-Demen regional model life table is selected as a death model; according to a preset birth sex ratio, an average life expectancy is set; the input parameter, the total fertility rate, the death model, the birth sex ratio and the average life expectancy are collectively input into the queue element method model, and the permanent population prediction of the to-be-predicted region is realized.

[0144] In some embodiments, the method of determining the differential order through the ADF test, preliminarily determining the range of the autoregressive order and the moving average order using the autocorrelation function and the partial autocorrelation function, and constructing the ARIMA model includes: taking the historical migrant population data as input, performing a stationarity test on the historical migrant population data, and determining the differential order required to stabilize the data through the ADF test; based on the stabilized data, determining the potential range of the moving average order by analyzing the tailing or truncation characteristics of the autocorrelation function, determining the potential range of the autoregressive order by analyzing the tailing or truncation characteristics of the partial autocorrelation function, and constructing the ARIMA model based on the differential order, the autoregressive order range, and the moving average order range.

[0145] In some embodiments, the method of optimizing the model parameters of the ARIMA model through cross-validation and selecting the optimal parameters based on the Akaike Information Criterion includes: dividing the historical migration population data into a training set and a validation set, cross-validating the ARIMA model of multiple parameter combinations, and evaluating the model performance by calculating the prediction error of the validation set; calculating the Akaike Information Criterion value for each parameter combination, and selecting the parameter combination with the smallest Akaike Information Criterion value as the optimal parameter of the ARIMA model.

[0146] In some embodiments, the optimized ARIMA model is used to fit the historical migrant population data to predict the migrant population in the target prediction time period to obtain the migrant population prediction result, including: using the ARIMA model to perform time series fitting on the historical migrant population data to extract trend, seasonality and random characteristics in the data; based on the fitted ARIMA model, an extrapolated prediction is performed on the migrant population in the target prediction time period, and the migrant population prediction result including the number of migrant population at each prediction time point is output.

[0147] In some embodiments, the selection of the western model of the Coldman regional model life table as the death model includes: based on the population death characteristics of the area to be predicted, selecting the western model in the Coldman regional model life table that matches the area to be predicted as a death probability calculation model, and the death model is used to predict the mortality rate of the population in each age group.

[0148] In some embodiments, setting the average life expectancy based on a preset sex ratio at birth includes: based on the sex ratio at birth corresponding to the area to be predicted, the sex ratio at birth is used to calculate the male-female ratio of newborns; based on preset empirical data on population life expectancy growth, setting the average life expectancy of each gender in the area to be predicted according to the average growth step, and the average life expectancy is used to correct the calculation parameters of the population survival probability.

[0149] In some embodiments, the inputting the input parameters into the cohort-component method model together with the total fertility rate, the death model, the birth sex ratio, and the average life expectancy, and realizing the resident population prediction of the to-be-predicted region comprises: based on the population balance equation of the cohort-component method, taking the migration population data of each age group, the total fertility rate, the mortality output by the death model, the birth sex ratio, and the average life expectancy as input parameters, calculating the number of the birth population, the death population, the migration population, and the existing population in each year of the target prediction period through the age- and gender-divided population dynamic simulation; and finally outputting the resident population prediction result of the to-be-predicted region in the target prediction period through iteratively calculating the population stock of each year.

[0150] The embodiment of the present application also provides a computer readable storage medium, which stores a computer program, and the computer program comprises program instructions. The processor executes the program instructions to realize any one of the population prediction methods based on the combination of the ARIMA model and the cohort-component method provided in the embodiments of the present application.

[0151] The computer readable storage medium can be an internal storage unit of the computer device, for example, a hard disk or a memory of the computer device. The computer readable storage medium can also be an external storage device of the computer device, for example, a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc.

[0152] The above merely describes the specific implementation of the present application, but the protection scope of the present application is not limited to this. Any person skilled in the art can easily think of various equivalent modifications or replacements within the technical range disclosed in the present application, and these modifications or replacements should be covered in the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A population forecasting method based on the combination of ARIMA model and cohort factor method, characterized by: The method comprises: Obtain historical migrant population data for the area to be predicted, determine the difference order through the ADF test, preliminarily determine the range of the autoregressive order and the moving average order using the autocorrelation function and the partial autocorrelation function, and construct an ARIMA model; optimize the model parameters of the ARIMA model through cross-validation, select the optimal parameters based on the Akaike Information Criterion, fit the historical migrant population data using the optimized ARIMA model, predict the migrant population in the target prediction time period, and obtain the migrant population prediction result; The migration population prediction result is used as input, combined with the age structure data of the floating population in the base year, to output the migration population data of each age group within the target prediction period; the migration population data of each age group is used as the input parameter of the migration population in the cohort factor method; According to the preset total fertility rate, the western model of the Coleman-Derman regional model life table is selected as the death model; the average life expectancy is set according to the preset sex ratio at birth; the input parameters are input into the cohort element method model together with the total fertility rate, death model, sex ratio at birth, and average life expectancy to realize the permanent population prediction of the area to be predicted.

2. The method according to claim 1, characterized in that The ADF test is used to determine the difference order, the autocorrelation function and the partial autocorrelation function are used to preliminarily determine the range of the autoregressive order and the moving average order, and the ARIMA model is constructed, including: Taking the historical migration population data as input, performing a stationarity test on the historical migration population data, and determining the difference order required to stabilize the data through an ADF test; Based on the stabilized data, the potential range of the moving average order is determined by analyzing the tailing or truncation characteristics of the autocorrelation function, and the potential range of the autoregressive order is determined by analyzing the tailing or truncation characteristics of the partial autocorrelation function. An ARIMA model is constructed based on the difference order, autoregressive order range, and moving average order range.

3. The method according to claim 1, characterized in that The method of optimizing the model parameters of the ARIMA model by cross-validation and selecting the optimal parameters based on the Akaike Information Criterion includes: Dividing the historical migration population data into a training set and a validation set, cross-validating the ARIMA model with multiple parameter combinations, and evaluating the model performance by calculating the prediction error of the validation set; The Akaike Information Criterion value is calculated for each parameter combination, and the parameter combination with the smallest Akaike Information Criterion value is selected as the optimal parameter of the ARIMA model.

4. The method according to claim 1, wherein The optimized ARIMA model is used to fit the historical migrant population data, and the migrant population in the target forecast time period is predicted to obtain the migrant population forecast result, including: Using the ARIMA model to perform time series fitting on the historical migration population data, and extracting trend, seasonality and randomness characteristics in the data; Based on the fitted ARIMA model, an extrapolated forecast of the migrant population within the target forecast period is conducted, and the forecast results of the migrant population including the number of migrant population at each forecast time point are output.

5. The method according to claim 1, wherein The western model of the Coleman-Derman regional model life table is selected as the death model, including: According to the population death characteristics of the area to be predicted, the western model in the Coleman-Derman regional model life table that matches the area to be predicted is selected as the death probability calculation model. The death model is used to predict the mortality rate of the population in each age group.

6. The method according to claim 1, characterized in that The setting of average life expectancy based on a preset sex ratio at birth includes: According to the birth sex ratio corresponding to the region to be predicted, the birth sex ratio is used to calculate the male-female ratio of newborns; Based on the preset empirical data on population life expectancy growth, the average life expectancy of each gender in the area to be predicted is set according to the average growth step. The average life expectancy is used to correct the calculation parameters of the population survival probability.

7. The method according to claim 1, characterized in that The step of inputting the input parameters together with the total fertility rate, the mortality model, the sex ratio at birth, and the average life expectancy into a cohort factor method model to achieve the resident population prediction of the area to be predicted includes: The population balance equation based on the cohort factor method takes the migrant population data of each age group, the total fertility rate, the mortality rate output by the mortality model, the sex ratio at birth, and the average life expectancy as input parameters. Through age- and sex-specific population dynamics simulation, the number of births, deaths, migrants, and the current population in each year of the target forecast period is calculated; By iteratively calculating the population stock of each year, the permanent population forecast result of the area to be predicted within the target prediction time period is finally output.

8. A population forecasting device based on the combination of ARIMA model and cohort factor method, characterized in that: The device comprises: A data acquisition unit is used to obtain historical migrant population data of the area to be predicted, determine the difference order through the ADF test, preliminarily determine the range of the autoregressive order and the moving average order using the autocorrelation function and the partial autocorrelation function, and construct an ARIMA model; optimize the model parameters of the ARIMA model through cross-validation, select the optimal parameters based on the Akaike Information Criterion, use the optimized ARIMA model to fit the historical migrant population data, predict the migrant population in the target prediction time period, and obtain the migrant population prediction result; A result input unit is used to take the migrant population prediction result as input, combine it with the age structure data of the floating population in the base year, and output the migrant population data of each age group within the target prediction time period; and use the migrant population data of each age group as the input parameter of the migrant population in the cohort factor method; The prediction completion unit is used to select the western model of the Coleman-Derman regional model life table as the death model based on the preset total fertility rate; set the average life expectancy based on the preset sex ratio at birth; and input the input parameters together with the total fertility rate, death model, sex ratio at birth, and average life expectancy into the cohort element method model to realize the permanent population prediction of the area to be predicted.

9. A computer device, characterized in that: The method comprises a memory and a processor, wherein the memory stores computer-readable instructions, and when the computer-readable instructions are executed by the processor, the processor executes the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer-readable instructions are executed by the processor, one or more processors are caused to perform the steps of the method according to any one of claims 1 to 7.

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